Appendix S4: Repeating Gillingham et al.’s (2012) analysis testing for an association
between EBC and MLH with a larger sample size
We repeated Gillingham et al.’s (2012) analysis but with the additional individuals genotyped
for this study using the software package R-2.15.3 (http://www.R-project.org). Namely we
modeled the response variable EBC according to MLH, cohort (1995, 1996, 1997 and 1998),
sex (female or male) and the two-way interaction between sex and cohort, using a linear
model with a Gaussian distribution. All possible candidate models were constructed. Model
selection relied on information-theoretic criteria and multi-model inference approach
(Burnham & Anderson 2002) which is recommended when dealing with observational data
(Johnson & Omland 2004). Akaike’s Information Criterion adjusted for small samples sizes
(AICc) was used for model interpretation. AICc weights (ω) were used to assess the relative
strength of support for models (Burnham & Anderson 2002; Johnson & Omland 2004). Only
the 10 top ranked models based on AICc are presented. Parameter estimates were calculated
using model averaging whereby regression coefficients are averaged across models with a
cumulative ω of 0.95, which are more robust when several models have similar support
(Burnham & Anderson 2002; Johnson & Omland 2004). The relative importance of each
predictor variable was estimated by summing the AIC weight (ΣAICω) in which that variable
appears across supported models (models with a cumulative ω of 0.95) (Burnham &
Anderson 2002; Symonds & Moussalli 2011). A summed Akaike weight value tends towards
1 if a particular predictor appears in all of the supported models. Conversely, a summed
Akaike weight value tends towards 0 if a particular predictor appears only in models with low
support (Burnham & Anderson 2002; Symonds & Moussalli 2011). A ΣAICω value is a
relative measure, its interpretation is strongly dependent on the data and the parameters used,
and its value is always > 0 even if there is no association between the parameter and the
response variable (Burnham & Anderson 2002, p. 345-347; Galipaud et al. submitted). We
therefore calculated a baseline ΣAICω for each parameter based on randomization methods
(10000 permutations; Burnham & Anderson 2002, p. 345-347; Galipaud et al. submitted).
This baseline ΣAICω is the estimated ΣAICω if the parameter has no association with the
response variable EBC and enables direct comparison with the observed ΣAICω in order to
weight the evidence of an association between the parameter and the response variable
(Burnham & Anderson 2002, p. 345-347; Galipaud et al. submitted).
Two models were retained as equivalent (Δ AICc < 2; Table S5), both of which
retained an effect of sex, cohort and the interaction between sex and cohort. There was strong
support for an association between EBC and sex (ΣAICω = 1; baseline ΣAICω = 0.39; Table
S6; Figure S4), cohort (ΣAICω = 1; baseline ΣAICω = 0.24; Table S6; Figure S4) and the
interaction between sex and cohort (ΣAICω = 1; baseline ΣAICω = 0.04; Table S6; Figure
S4). Although MLH was retained in one of the two parsimonious models, the ΣAICω
suggests there was no evidence of an association between EBC and MLH (ΣAICω = 0.37;
baseline ΣAICω = 0.37; Table S5) and 95% confidence intervals of the slope largely
overlapped zero (Table S6).
Table S5 : Models of early body condition of greater flamingos with number of parameters (k), log-likelihood
(LL), AICc of the models, change in AICc compared to the best-ranked model (Δ AICc), Akaike model weights
(ω) and cumulative Akaike weight (Cum. ω) given. The full model included sex, cohort, microsatellite MLH,
and the two-ways interactions between sex and cohort.
Model rank
Model
K
LL
AICc
Δ AICc
ω
Cum. ω
R2
1
Cohort+Sex+Cohort*Sex
9
-7031.35
14080.9
0
0.563
0.563
0.13
2
Cohort+Sex+Cohort*Sex +MLH
10
-7030.84
14081.9
1.02
0.338
0.901
6
0.13
3
Cohort+Sex
6
-7036.65
14085.4
4.49
0.06
0.961
7
0.12
4
Cohort+Sex+MLH
7
-7036.05
14086.2
5.32
0.039
1
7
0.12
5
Cohort
5
-7043.28
14096.6
15.74
0
1
8
0.11
6
Cohort+MLH
6
-7042.67
14097.4
16.53
0
1
5
0.11
7
Sex +MLH
4
-7099.44
14206.9
126.04
0
1
6
0.01
8
Sex
3
-7100.55
14207.1
126.24
0
1
3
0.01
9
MLH
3
-7104.82
14215.7
134.78
0
1
1
0.00
10
Intercept
2
-7105.96
14215.9
135.05
0
1
20.00
0
Table S6 : Model averaged parameter estimates of models predicting early body condition of greater
flamingos. See table S5 for descriptions of models. The summed AIC weight of each parameter
(ΣAICω) and baseline summed AIC weight (baseline ΣAICω), calculated as the estimated ΣAICω if
parameter has no association with early body condition, are also given.
Model-averaged Estimate
Adjusted S.E.
95 % C.I.
2126.73
37.66
2052.91, 2200.54
1996
207.13
39.00
130.69, 283.57
1997
225.82
28.73
169.51, 282.13
1998
181.84
28.21
126.56, 237.12
Intercept (1995, Females)
Cohort
Sex
Males
-61.49
35.89
Baseline
ΣAICω
1
0.24
1
0.39
1
0.04
0.37
0.37
-131.84, 8.86
Cohort×Sex:
1996 (Males)
-110.99
57.61
-223.9, 1.91
1997 (Males)
52.46
43.42
-32.64, 137.56
1998 (Males)
-1.00
43.94
-87.12, 85.12
-54.38
54.19
-160.59, 51.83
0
200
500
800
1100
1400
1700
2000
2300
MLH
ΣAICω
Female
1995(100)
Male
1995 (75)
Female
1996 (57)
Male
1996 (52)
Female
1997 (202)
Male
1997 (171)
Female
1998 (228)
Male
1998 (138)
Sex / Cohort (sample size)
Figure S4 : Adjusted mean early body condition (±SEM) of greater flamingo chicks according to
cohort and sex (using model 1 in Table S5). Sample sizes are indicated within brackets.
References
Alho JS, Välimäki K, Merilä J (2010) Rhh: an R extension for estimating multilocus
heterozygosity and heterozygosity–heterozygosity correlation. Molecular Ecology
Resources, 10, 720–722.
Amos W, Wilmer JW, Fullard K et al. (2001) The influence of parental relatedness on
reproductive success. Proceedings of the Royal Society of London. Series B:
Biological Sciences, 268, 2021–2027.
Aparicio JM, Ortego J, Cordero PJ (2006) What should we weigh to estimate heterozygosity,
alleles or loci? Molecular Ecology, 15, 4659–4665.
Balloux F, Amos W, Coulson T (2004) Does heterozygosity estimate inbreeding in real
populations? Molecular Ecology, 13, 3021–3031.
Burnham K, Anderson D (2002) Model Selection and Multi-Model Inference - A Practical
Information-Theoretic Approach. Springer, New York.
Coltman DW, Pilkington JG, Smith JA, Pemberton JM (1999) Parasite-Mediated Selection
against Inbred Soay Sheep in a Free-Living, Island Population. Evolution, 53, 1259.
Galipaud M, Gillingham MAF, Morgan D, Dechaume-Moncharmont F-X (submitted)
Caution in the use of Akaike sums of weights for interpretation of parameter
importance in model averaging.
Gillingham MAF, Béchet A, Geraci J et al. (2012) Genetic polymorphism in dopamine
receptor D4 is associated with early body condition in a large population of greater
flamingos, Phoenicopterus roseus. Molecular Ecology, 21, 4024–4037.
Johnson JB, Omland KS (2004) Model selection in ecology and evolution. Trends in Ecology
& Evolution, 19, 101–108.
Sanz-Aguilar A, Béchet A, Germain C, Johnson AR, Pradel R (2012) To leave or not to leave:
survival trade-offs between different migratory strategies in the greater flamingo.
Journal of Animal Ecology, 81, 1171–1182.
Symonds MRE, Moussalli A (2011) A brief guide to model selection, multimodel inference
and model averaging in behavioural ecology using Akaike’s information criterion.
Behavioral Ecology and Sociobiology, 65, 13–21.